To solve the trajectory tracking problem for quadrotor UAV with control input saturation, a fuzzy adaptive dynamic surface control(DSC) scheme is proposed in the presence of the model uncertainties and the unknown external disturbances. Firstly, the disturbance observer is introduced to estimate the compound perturbation term of the position model, and the fuzzy system is designed to approximate the uncertainties and external disturbance of the attitude model. Then the hyperbolic tangent function and a constructed aid system are introduced to process the control input saturation problem. Furthermore, a novelty dynamic controller is designed based on the backstepping method with the dynamic surface technique, which can reduce the complexity of the control algorithm. Finally, by using Lyapunov analysis, it is proved that all signals of the closed-loop trajectory tracking system are the uniformly ultimate boundedness using the proposed control strategy. The simulation results on the DJI M100 aircraft model show that the designed controller can achieve strongly robust to model uncertainties and unknown external disturbances. Moreover, the proposed method can avoid the actuator failures caused by input saturation, and realize the trajectory tracking control accurately.